Analytical solutions for protective filters based on soil-retention and permeability criteria with respect to the phenomenon of soil boiling

For the successful performance of a granular filter medium, existing design guidelines, which are based on the particle size distribution (PSD) characteristics of the base soil and filter medium, require two contradictory conditions to be satisfied, viz., soil retention and permeability. In spite of the wider applicability of these guidelines, it is well recognized that (i) they are applicable to a particular range of soils tested in the laboratory, (ii) the design procedures do not include performance-based selection criteria, and (iii) there are no means to establish the sensitivity of the important variables influencing performance. In the present work, analytical solutions are developed to obtain a factor of safety with respect to soil-retention and permeability criteria for a base soil - filter medium system subjected to a soil boiling condition. The proposed analytical solutions take into consideration relevant geotechnical properties such as void ratio, permeability, dry unit weight, effective friction angle, shape and size of soil particles, seepage discharge, and existing hydraulic gradient. The solution is validated through example applications and experimental results, and it is established that it can be used successfully in the selection as well as design of granular filters and can be applied to all types of base soils.

Doubly spectral stochastic finite element method (DSSFEM) for random field problems

Uncertainties in complex dynamic systems play an important role in the prediction of a dynamic response in the mid- and high-frequency ranges. For distributed parameter systems, parametric uncertainties can be represented by random fields leading to stochastic partial differential equations. Over the past two decades, the spectral stochastic finite-element method has been developed to discretize the random fields and solve such problems. On the other hand, for deterministic distributed parameter linear dynamic systems, the spectral finite-element method has been developed to efficiently solve the problem in the frequency domain. In spite of the fact that both approaches use spectral decomposition (one for the random fields and the other for the dynamic displacement fields), very little overlap between them has been reported in literature. In this paper, these two spectral techniques are unified with the aim that the unified approach would outperform any of the spectral methods considered on their own. An exponential autocorrelation function for the random fields, a frequency-dependent stochastic element stiffness, and mass matrices are derived for the axial and bending vibration of rods. Closed-form exact expressions are derived by using the Karhunen-Loève expansion. Numerical examples are given to illustrate the unified spectral approach.

Beta-structure of polypeptides in non-aqueous solutions. I. Spectral characteristics of the polypeptide backbone

The optical rotatory features of the beta-structure of the polypeptides in non-aqueous solutions and films cast from these solutions have been investigated. The beta-structure of poly-S-benzyl-L-cysteine, poly-S-carbobenzoxy-L-cysteine and poly-S-benzyl-L-cysteine, poly-S-carbobenzoxy-L-cysteine and poly-O-carbo-bands of their films. The optical rotatory dispersion (ORD) and circular dichroism (CD) spectra of these polypeptides are found to be very similar in both film and solution. In solvents promoting the beta-structure, the polypeptides are characterized by CD troughs in the n-pi* transition region of the peptide chromophore. The ORD spectra are found to be positive in sign throughout the visible and accessible ultraviolet regions and are interpreted in terms of the possible existence of a relatively much larger positive pi-pi* CD bands as compared with the negative n-pi* band. The rotatory data obtained in the non-aqueous solution are compared with those obtained for other poly peptides in aqueous solutions, with respect to the type and extent of beta-structure present.

Beta-structure of polypeptides in non-aqueous solutions. II. Side-chain orientation

The specific side-chain orientations of the phenyl group in the polypeptides poly-S-benzyl-L-cysteine, poly-S-carbobenzoxy-L-cysteine and poly-O-carbobenzoxy-L-serine in the beta-structure have been studied by spectral measurements in solutions. All the three polypeptides exhibit aromatic CD bands, indicating the asymmetric placement of the side-chain phenyl rings when the polypeptide backbone takes up the antiparallel beta-structure. Supporting evidence for this is derived from n.m.r. spectra of the polypeptides, which show upfield shift of the phenyl protons due to the stacking of the aromatic rings. Molecular model building studies reveal the stacking of alternate phenyl groups along the polypeptide chain.